Question

the equal side of the isosceles triangle are 12cm and the perimeter is 30cm the area of this triangle is ​

Answer 1

★ Question ★

The equal sides of the isosceles triangle are 12cm, and the perimeter is 30cm.The area of the triangle is :

Answer :-

The area of isosceles triangle is 9√15 cm².

★ Given :-

☞ 2 equal sides of the triangle = 12 cm

☞ Perimeter = 30 cm

★ To be calculated :-

☞ The area of isosceles triangle.

★ Solution :-

✒ We know that ,

• Perimeter of Triangle = ( a + b + c )

✒ a ↠ 12 cm.

✒ b ↠ 12 cm.

✒ c ↠ ?

30 = 12 + 12 + c

c = 30 - 24

c = 6 cm

Therefore,

✒ The third side of isosceles triangle is 6 cm.

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➤ Now,

Semi - Perimeter of triangle = $\frac{a + b + c}{2}$

Semi - Perimeter of triangle = $\frac{12 + 12 + 6}{2}$

Semi - Perimeter of triangle = $\frac{30}{2}$

Semi -Perimeter of triangle = 15 cm.

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Area of triangle = √s (s - a) (s - b) (s - c)

✒s ( semi - perimeter ) ↠15 cm

✒a ↠12 cm

✒b ↠12 cm

✒c ↠ 6 cm

Now ,

put the values in above given formula

Area of triangle = 15(15 - 12)(15 - 12)(15 - 6)

Area of triangle = √15 × 3 × 3 × 9

Hence,

➤ The area of isosceles triangle is 9√15 cm².

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